TSTP Solution File: KLE064+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE064+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 01:36:59 EDT 2022
% Result : Theorem 24.83s 25.25s
% Output : Refutation 24.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE064+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Thu Jun 16 09:51:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 19.59/19.97 *** allocated 10000 integers for termspace/termends
% 19.59/19.97 *** allocated 10000 integers for clauses
% 19.59/19.97 *** allocated 10000 integers for justifications
% 19.59/19.97 Bliksem 1.12
% 19.59/19.97
% 19.59/19.97
% 19.59/19.97 Automatic Strategy Selection
% 19.59/19.97
% 19.59/19.97
% 19.59/19.97 Clauses:
% 19.59/19.97
% 19.59/19.97 { addition( X, Y ) = addition( Y, X ) }.
% 19.59/19.97 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 19.59/19.97 { addition( X, zero ) = X }.
% 19.59/19.97 { addition( X, X ) = X }.
% 19.59/19.97 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 19.59/19.97 multiplication( X, Y ), Z ) }.
% 19.59/19.97 { multiplication( X, one ) = X }.
% 19.59/19.97 { multiplication( one, X ) = X }.
% 19.59/19.97 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 19.59/19.97 , multiplication( X, Z ) ) }.
% 19.59/19.97 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 19.59/19.97 , multiplication( Y, Z ) ) }.
% 19.59/19.97 { multiplication( X, zero ) = zero }.
% 19.59/19.97 { multiplication( zero, X ) = zero }.
% 19.59/19.97 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 19.59/19.97 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 19.59/19.97 { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 19.59/19.97 ( X ), X ) }.
% 19.59/19.97 { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 19.59/19.97 ) ) }.
% 19.59/19.97 { addition( domain( X ), one ) = one }.
% 19.59/19.97 { domain( zero ) = zero }.
% 19.59/19.97 { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 19.59/19.97 { addition( domain( skol1 ), domain( skol2 ) ) = domain( skol2 ) }.
% 19.59/19.97 { ! addition( skol1, multiplication( domain( skol2 ), skol1 ) ) =
% 19.59/19.97 multiplication( domain( skol2 ), skol1 ) }.
% 19.59/19.97
% 19.59/19.97 percentage equality = 0.909091, percentage horn = 1.000000
% 19.59/19.97 This is a pure equality problem
% 19.59/19.97
% 19.59/19.97
% 19.59/19.97
% 19.59/19.97 Options Used:
% 19.59/19.97
% 19.59/19.97 useres = 1
% 19.59/19.97 useparamod = 1
% 19.59/19.97 useeqrefl = 1
% 19.59/19.97 useeqfact = 1
% 19.59/19.97 usefactor = 1
% 19.59/19.97 usesimpsplitting = 0
% 19.59/19.97 usesimpdemod = 5
% 19.59/19.97 usesimpres = 3
% 19.59/19.97
% 19.59/19.97 resimpinuse = 1000
% 19.59/19.97 resimpclauses = 20000
% 19.59/19.97 substype = eqrewr
% 19.59/19.97 backwardsubs = 1
% 19.59/19.97 selectoldest = 5
% 19.59/19.97
% 19.59/19.97 litorderings [0] = split
% 19.59/19.97 litorderings [1] = extend the termordering, first sorting on arguments
% 19.59/19.97
% 19.59/19.97 termordering = kbo
% 19.59/19.97
% 19.59/19.97 litapriori = 0
% 19.59/19.97 termapriori = 1
% 19.59/19.97 litaposteriori = 0
% 19.59/19.97 termaposteriori = 0
% 19.59/19.97 demodaposteriori = 0
% 19.59/19.97 ordereqreflfact = 0
% 19.59/19.97
% 19.59/19.97 litselect = negord
% 19.59/19.97
% 19.59/19.97 maxweight = 15
% 19.59/19.97 maxdepth = 30000
% 19.59/19.97 maxlength = 115
% 19.59/19.97 maxnrvars = 195
% 19.59/19.97 excuselevel = 1
% 19.59/19.97 increasemaxweight = 1
% 19.59/19.97
% 19.59/19.97 maxselected = 10000000
% 19.59/19.97 maxnrclauses = 10000000
% 19.59/19.97
% 19.59/19.97 showgenerated = 0
% 19.59/19.97 showkept = 0
% 19.59/19.97 showselected = 0
% 19.59/19.97 showdeleted = 0
% 19.59/19.97 showresimp = 1
% 19.59/19.97 showstatus = 2000
% 19.59/19.97
% 19.59/19.97 prologoutput = 0
% 19.59/19.97 nrgoals = 5000000
% 19.59/19.97 totalproof = 1
% 19.59/19.97
% 19.59/19.97 Symbols occurring in the translation:
% 19.59/19.97
% 19.59/19.97 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 19.59/19.97 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 19.59/19.97 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 19.59/19.97 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 19.59/19.97 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 19.59/19.97 addition [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 19.59/19.97 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 19.59/19.97 multiplication [40, 2] (w:1, o:47, a:1, s:1, b:0),
% 19.59/19.97 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 19.59/19.97 leq [42, 2] (w:1, o:46, a:1, s:1, b:0),
% 19.59/19.97 domain [44, 1] (w:1, o:20, a:1, s:1, b:0),
% 19.59/19.97 skol1 [46, 0] (w:1, o:13, a:1, s:1, b:1),
% 19.59/19.97 skol2 [47, 0] (w:1, o:14, a:1, s:1, b:1).
% 19.59/19.97
% 19.59/19.97
% 19.59/19.97 Starting Search:
% 19.59/19.97
% 19.59/19.97 *** allocated 15000 integers for clauses
% 19.59/19.97 *** allocated 22500 integers for clauses
% 19.59/19.97 *** allocated 33750 integers for clauses
% 19.59/19.97 *** allocated 50625 integers for clauses
% 19.59/19.97 *** allocated 75937 integers for clauses
% 19.59/19.97 *** allocated 15000 integers for termspace/termends
% 19.59/19.97 Resimplifying inuse:
% 19.59/19.97 Done
% 19.59/19.97
% 19.59/19.97 *** allocated 22500 integers for termspace/termends
% 19.59/19.97 *** allocated 113905 integers for clauses
% 19.59/19.97 *** allocated 170857 integers for clauses
% 19.59/19.97 *** allocated 33750 integers for termspace/termends
% 19.59/19.97
% 19.59/19.97 Intermediate Status:
% 19.59/19.97 Generated: 18098
% 19.59/19.97 Kept: 2001
% 19.59/19.97 Inuse: 299
% 19.59/19.97 Deleted: 34
% 19.59/19.97 Deletedinuse: 11
% 19.59/19.97
% 19.59/19.97 Resimplifying inuse:
% 19.59/19.97 Done
% 19.59/19.97
% 19.59/19.97 *** allocated 50625 integers for termspace/termends
% 19.59/19.97 Resimplifying inuse:
% 19.59/19.97 Done
% 19.59/19.97
% 19.59/19.97 *** allocated 256285 integers for clauses
% 19.59/19.97
% 19.59/19.97 Intermediate Status:
% 19.59/19.97 Generated: 40399
% 19.59/19.97 Kept: 4016
% 19.59/19.97 Inuse: 401
% 19.59/19.97 Deleted: 60
% 19.59/19.97 Deletedinuse: 29
% 19.59/19.97
% 19.59/19.97 Resimplifying inuse:
% 19.59/19.97 Done
% 19.59/19.97
% 19.59/19.97 *** allocated 75937 integers for termspace/termends
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 *** allocated 384427 integers for clauses
% 24.83/25.25 *** allocated 113905 integers for termspace/termends
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 64972
% 24.83/25.25 Kept: 6019
% 24.83/25.25 Inuse: 551
% 24.83/25.25 Deleted: 99
% 24.83/25.25 Deletedinuse: 31
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 *** allocated 576640 integers for clauses
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 103389
% 24.83/25.25 Kept: 8208
% 24.83/25.25 Inuse: 661
% 24.83/25.25 Deleted: 120
% 24.83/25.25 Deletedinuse: 33
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 *** allocated 170857 integers for termspace/termends
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 122568
% 24.83/25.25 Kept: 10226
% 24.83/25.25 Inuse: 665
% 24.83/25.25 Deleted: 121
% 24.83/25.25 Deletedinuse: 33
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 *** allocated 256285 integers for termspace/termends
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 154396
% 24.83/25.25 Kept: 12230
% 24.83/25.25 Inuse: 747
% 24.83/25.25 Deleted: 128
% 24.83/25.25 Deletedinuse: 33
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 *** allocated 864960 integers for clauses
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 184706
% 24.83/25.25 Kept: 14241
% 24.83/25.25 Inuse: 789
% 24.83/25.25 Deleted: 132
% 24.83/25.25 Deletedinuse: 37
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 211023
% 24.83/25.25 Kept: 16266
% 24.83/25.25 Inuse: 854
% 24.83/25.25 Deleted: 134
% 24.83/25.25 Deletedinuse: 37
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 *** allocated 384427 integers for termspace/termends
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 245106
% 24.83/25.25 Kept: 18278
% 24.83/25.25 Inuse: 917
% 24.83/25.25 Deleted: 135
% 24.83/25.25 Deletedinuse: 37
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 *** allocated 1297440 integers for clauses
% 24.83/25.25 Resimplifying clauses:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 285255
% 24.83/25.25 Kept: 20293
% 24.83/25.25 Inuse: 1006
% 24.83/25.25 Deleted: 2809
% 24.83/25.25 Deletedinuse: 48
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 307490
% 24.83/25.25 Kept: 22436
% 24.83/25.25 Inuse: 1058
% 24.83/25.25 Deleted: 2809
% 24.83/25.25 Deletedinuse: 48
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 339416
% 24.83/25.25 Kept: 24447
% 24.83/25.25 Inuse: 1118
% 24.83/25.25 Deleted: 2809
% 24.83/25.25 Deletedinuse: 48
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 382149
% 24.83/25.25 Kept: 26473
% 24.83/25.25 Inuse: 1198
% 24.83/25.25 Deleted: 2811
% 24.83/25.25 Deletedinuse: 49
% 24.83/25.25
% 24.83/25.25 *** allocated 576640 integers for termspace/termends
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 *** allocated 1946160 integers for clauses
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 428292
% 24.83/25.25 Kept: 28475
% 24.83/25.25 Inuse: 1286
% 24.83/25.25 Deleted: 2814
% 24.83/25.25 Deletedinuse: 51
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 445372
% 24.83/25.25 Kept: 30722
% 24.83/25.25 Inuse: 1303
% 24.83/25.25 Deleted: 2815
% 24.83/25.25 Deletedinuse: 51
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 475386
% 24.83/25.25 Kept: 32756
% 24.83/25.25 Inuse: 1343
% 24.83/25.25 Deleted: 2815
% 24.83/25.25 Deletedinuse: 51
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 520003
% 24.83/25.25 Kept: 34912
% 24.83/25.25 Inuse: 1389
% 24.83/25.25 Deleted: 2815
% 24.83/25.25 Deletedinuse: 51
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 555000
% 24.83/25.25 Kept: 36916
% 24.83/25.25 Inuse: 1431
% 24.83/25.25 Deleted: 2815
% 24.83/25.25 Deletedinuse: 51
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 *** allocated 864960 integers for termspace/termends
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 585039
% 24.83/25.25 Kept: 39037
% 24.83/25.25 Inuse: 1447
% 24.83/25.25 Deleted: 2815
% 24.83/25.25 Deletedinuse: 51
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying clauses:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 613576
% 24.83/25.25 Kept: 41088
% 24.83/25.25 Inuse: 1486
% 24.83/25.25 Deleted: 4434
% 24.83/25.25 Deletedinuse: 51
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 646886
% 24.83/25.25 Kept: 43121
% 24.83/25.25 Inuse: 1554
% 24.83/25.25 Deleted: 4438
% 24.83/25.25 Deletedinuse: 54
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 *** allocated 2919240 integers for clauses
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 670272
% 24.83/25.25 Kept: 45127
% 24.83/25.25 Inuse: 1588
% 24.83/25.25 Deleted: 4440
% 24.83/25.25 Deletedinuse: 54
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 707316
% 24.83/25.25 Kept: 47132
% 24.83/25.25 Inuse: 1643
% 24.83/25.25 Deleted: 4440
% 24.83/25.25 Deletedinuse: 54
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 746880
% 24.83/25.25 Kept: 49137
% 24.83/25.25 Inuse: 1696
% 24.83/25.25 Deleted: 4441
% 24.83/25.25 Deletedinuse: 55
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 769616
% 24.83/25.25 Kept: 51152
% 24.83/25.25 Inuse: 1725
% 24.83/25.25 Deleted: 4443
% 24.83/25.25 Deletedinuse: 57
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Intermediate Status:
% 24.83/25.25 Generated: 838939
% 24.83/25.25 Kept: 53188
% 24.83/25.25 Inuse: 1796
% 24.83/25.25 Deleted: 4443
% 24.83/25.25 Deletedinuse: 57
% 24.83/25.25
% 24.83/25.25 Resimplifying inuse:
% 24.83/25.25 Done
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Bliksems!, er is een bewijs:
% 24.83/25.25 % SZS status Theorem
% 24.83/25.25 % SZS output start Refutation
% 24.83/25.25
% 24.83/25.25 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 24.83/25.25 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 24.83/25.25 addition( Z, Y ), X ) }.
% 24.83/25.25 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 24.83/25.25 (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication( Y, Z ) )
% 24.83/25.25 ==> multiplication( multiplication( X, Y ), Z ) }.
% 24.83/25.25 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 24.83/25.25 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 24.83/25.25 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 24.83/25.25 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 24.83/25.25 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 24.83/25.25 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 24.83/25.25 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 24.83/25.25 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 24.83/25.25 (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 24.83/25.25 ) ==> multiplication( domain( X ), X ) }.
% 24.83/25.25 (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain( Y ) ) )
% 24.83/25.25 ==> domain( multiplication( X, Y ) ) }.
% 24.83/25.25 (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> one }.
% 24.83/25.25 (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y ) ) ==>
% 24.83/25.25 domain( addition( X, Y ) ) }.
% 24.83/25.25 (18) {G1,W7,D4,L1,V0,M1} I;d(17) { domain( addition( skol1, skol2 ) ) ==>
% 24.83/25.25 domain( skol2 ) }.
% 24.83/25.25 (19) {G0,W11,D5,L1,V0,M1} I { ! addition( skol1, multiplication( domain(
% 24.83/25.25 skol2 ), skol1 ) ) ==> multiplication( domain( skol2 ), skol1 ) }.
% 24.83/25.25 (21) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) ) ==> one }.
% 24.83/25.25 (24) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X ) ==>
% 24.83/25.25 addition( Y, X ) }.
% 24.83/25.25 (25) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 24.83/25.25 addition( addition( Y, Z ), X ) }.
% 24.83/25.25 (31) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 24.83/25.25 (35) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y, leq( X, Y )
% 24.83/25.25 }.
% 24.83/25.25 (38) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, addition( Y, Z ) )
% 24.83/25.25 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 24.83/25.25 ( X, Z ) ) }.
% 24.83/25.25 (51) {G1,W12,D4,L2,V3,M2} P(11,1) { addition( addition( Z, X ), Y ) ==>
% 24.83/25.25 addition( Z, Y ), ! leq( X, Y ) }.
% 24.83/25.25 (53) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 24.83/25.25 }.
% 24.83/25.25 (78) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition( X, Z ), Y )
% 24.83/25.25 ==> multiplication( Z, Y ), leq( multiplication( X, Y ), multiplication
% 24.83/25.25 ( Z, Y ) ) }.
% 24.83/25.25 (81) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication( Y, X ) ) =
% 24.83/25.25 multiplication( addition( one, Y ), X ) }.
% 24.83/25.25 (141) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) ) ==> domain(
% 24.83/25.25 X ) }.
% 24.83/25.25 (199) {G1,W6,D4,L1,V0,M1} R(19,11) { ! leq( skol1, multiplication( domain(
% 24.83/25.25 skol2 ), skol1 ) ) }.
% 24.83/25.25 (251) {G2,W5,D3,L1,V2,M1} R(24,35) { leq( X, addition( Y, X ) ) }.
% 24.83/25.25 (263) {G3,W5,D3,L1,V2,M1} P(0,251) { leq( Y, addition( Y, X ) ) }.
% 24.83/25.25 (266) {G4,W7,D4,L1,V2,M1} P(17,263) { leq( domain( X ), domain( addition( X
% 24.83/25.25 , Y ) ) ) }.
% 24.83/25.25 (286) {G3,W7,D4,L1,V3,M1} P(25,251) { leq( Z, addition( addition( Y, Z ), X
% 24.83/25.25 ) ) }.
% 24.83/25.25 (420) {G2,W10,D3,L2,V3,M2} P(11,38);q { leq( multiplication( Z, X ),
% 24.83/25.25 multiplication( Z, Y ) ), ! leq( X, Y ) }.
% 24.83/25.25 (422) {G2,W6,D4,L1,V2,M1} P(15,38);q;d(5) { leq( multiplication( Y, domain
% 24.83/25.25 ( X ) ), Y ) }.
% 24.83/25.25 (806) {G2,W9,D2,L3,V2,M3} P(53,11) { ! leq( X, Y ), X = Y, ! leq( Y, X )
% 24.83/25.25 }.
% 24.83/25.25 (906) {G4,W8,D3,L2,V3,M2} P(51,286) { leq( Y, addition( X, Z ) ), ! leq( Y
% 24.83/25.25 , Z ) }.
% 24.83/25.25 (1089) {G5,W5,D3,L1,V0,M1} P(18,266) { leq( domain( skol1 ), domain( skol2
% 24.83/25.25 ) ) }.
% 24.83/25.25 (1532) {G2,W6,D4,L1,V2,M1} P(15,78);q;d(6) { leq( multiplication( domain( X
% 24.83/25.25 ), Y ), Y ) }.
% 24.83/25.25 (1539) {G3,W8,D5,L1,V2,M1} R(1532,53) { addition( X, multiplication( domain
% 24.83/25.25 ( Y ), X ) ) ==> X }.
% 24.83/25.25 (1695) {G2,W6,D4,L1,V1,M1} P(81,13);d(21);d(6) { multiplication( domain( X
% 24.83/25.25 ), X ) ==> X }.
% 24.83/25.25 (1722) {G3,W8,D4,L1,V1,M1} P(141,1695) { multiplication( domain( X ),
% 24.83/25.25 domain( X ) ) ==> domain( X ) }.
% 24.83/25.25 (6325) {G5,W9,D4,L2,V3,M2} P(1539,906) { leq( Z, X ), ! leq( Z,
% 24.83/25.25 multiplication( domain( Y ), X ) ) }.
% 24.83/25.25 (20864) {G6,W9,D4,L1,V1,M1} R(420,1089) { leq( multiplication( X, domain(
% 24.83/25.25 skol1 ) ), multiplication( X, domain( skol2 ) ) ) }.
% 24.83/25.25 (25587) {G7,W8,D4,L1,V0,M1} P(1722,20864) { leq( domain( skol1 ),
% 24.83/25.25 multiplication( domain( skol1 ), domain( skol2 ) ) ) }.
% 24.83/25.25 (25618) {G8,W8,D4,L1,V0,M1} R(25587,806);r(422) { multiplication( domain(
% 24.83/25.25 skol1 ), domain( skol2 ) ) ==> domain( skol1 ) }.
% 24.83/25.25 (25882) {G9,W8,D5,L1,V0,M1} P(25618,14);d(141) { domain( multiplication(
% 24.83/25.25 domain( skol1 ), skol2 ) ) ==> domain( skol1 ) }.
% 24.83/25.25 (29163) {G6,W9,D5,L1,V1,M1} R(6325,199);d(4) { ! leq( skol1, multiplication
% 24.83/25.25 ( multiplication( domain( X ), domain( skol2 ) ), skol1 ) ) }.
% 24.83/25.25 (54616) {G10,W0,D0,L0,V0,M0} P(25882,29163);d(25618);d(1695);r(31) { }.
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 % SZS output end Refutation
% 24.83/25.25 found a proof!
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Unprocessed initial clauses:
% 24.83/25.25
% 24.83/25.25 (54618) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 24.83/25.25 (54619) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 24.83/25.25 ( addition( Z, Y ), X ) }.
% 24.83/25.25 (54620) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 24.83/25.25 (54621) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 24.83/25.25 (54622) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 24.83/25.25 = multiplication( multiplication( X, Y ), Z ) }.
% 24.83/25.25 (54623) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 24.83/25.25 (54624) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 24.83/25.25 (54625) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 24.83/25.25 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 24.83/25.25 (54626) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 24.83/25.25 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 24.83/25.25 (54627) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 24.83/25.25 (54628) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 24.83/25.25 (54629) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 24.83/25.25 (54630) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 24.83/25.25 (54631) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain( X ), X
% 24.83/25.25 ) ) = multiplication( domain( X ), X ) }.
% 24.83/25.25 (54632) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) = domain(
% 24.83/25.25 multiplication( X, domain( Y ) ) ) }.
% 24.83/25.25 (54633) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one }.
% 24.83/25.25 (54634) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 24.83/25.25 (54635) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) = addition(
% 24.83/25.25 domain( X ), domain( Y ) ) }.
% 24.83/25.25 (54636) {G0,W8,D4,L1,V0,M1} { addition( domain( skol1 ), domain( skol2 ) )
% 24.83/25.25 = domain( skol2 ) }.
% 24.83/25.25 (54637) {G0,W11,D5,L1,V0,M1} { ! addition( skol1, multiplication( domain(
% 24.83/25.25 skol2 ), skol1 ) ) = multiplication( domain( skol2 ), skol1 ) }.
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Total Proof:
% 24.83/25.25
% 24.83/25.25 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 24.83/25.25 ) }.
% 24.83/25.25 parent0: (54618) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 24.83/25.25 }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 24.83/25.25 ==> addition( addition( Z, Y ), X ) }.
% 24.83/25.25 parent0: (54619) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 24.83/25.25 addition( addition( Z, Y ), X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 24.83/25.25 parent0: (54621) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 24.83/25.25 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 24.83/25.25 parent0: (54622) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication
% 24.83/25.25 ( Y, Z ) ) = multiplication( multiplication( X, Y ), Z ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 24.83/25.25 parent0: (54623) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 24.83/25.25 parent0: (54624) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54663) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 24.83/25.25 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 24.83/25.25 parent0[0]: (54625) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 24.83/25.25 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 24.83/25.25 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 24.83/25.25 parent0: (54663) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 24.83/25.25 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54671) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 24.83/25.25 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 24.83/25.25 parent0[0]: (54626) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 24.83/25.25 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 24.83/25.25 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 24.83/25.25 parent0: (54671) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 24.83/25.25 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 24.83/25.25 ==> Y }.
% 24.83/25.25 parent0: (54629) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 24.83/25.25 }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 1 ==> 1
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 24.83/25.25 , Y ) }.
% 24.83/25.25 parent0: (54630) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 24.83/25.25 }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 1 ==> 1
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 24.83/25.25 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 24.83/25.25 parent0: (54631) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication(
% 24.83/25.25 domain( X ), X ) ) = multiplication( domain( X ), X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54721) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain(
% 24.83/25.25 Y ) ) ) = domain( multiplication( X, Y ) ) }.
% 24.83/25.25 parent0[0]: (54632) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y )
% 24.83/25.25 ) = domain( multiplication( X, domain( Y ) ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X,
% 24.83/25.25 domain( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 24.83/25.25 parent0: (54721) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain
% 24.83/25.25 ( Y ) ) ) = domain( multiplication( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 24.83/25.25 one }.
% 24.83/25.25 parent0: (54633) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one
% 24.83/25.25 }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54753) {G0,W10,D4,L1,V2,M1} { addition( domain( X ), domain( Y )
% 24.83/25.25 ) = domain( addition( X, Y ) ) }.
% 24.83/25.25 parent0[0]: (54635) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) =
% 24.83/25.25 addition( domain( X ), domain( Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 24.83/25.25 ) ) ==> domain( addition( X, Y ) ) }.
% 24.83/25.25 parent0: (54753) {G0,W10,D4,L1,V2,M1} { addition( domain( X ), domain( Y )
% 24.83/25.25 ) = domain( addition( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54793) {G1,W7,D4,L1,V0,M1} { domain( addition( skol1, skol2 ) )
% 24.83/25.25 = domain( skol2 ) }.
% 24.83/25.25 parent0[0]: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 24.83/25.25 ) ) ==> domain( addition( X, Y ) ) }.
% 24.83/25.25 parent1[0; 1]: (54636) {G0,W8,D4,L1,V0,M1} { addition( domain( skol1 ),
% 24.83/25.25 domain( skol2 ) ) = domain( skol2 ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := skol1
% 24.83/25.25 Y := skol2
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (18) {G1,W7,D4,L1,V0,M1} I;d(17) { domain( addition( skol1,
% 24.83/25.25 skol2 ) ) ==> domain( skol2 ) }.
% 24.83/25.25 parent0: (54793) {G1,W7,D4,L1,V0,M1} { domain( addition( skol1, skol2 ) )
% 24.83/25.25 = domain( skol2 ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (19) {G0,W11,D5,L1,V0,M1} I { ! addition( skol1,
% 24.83/25.25 multiplication( domain( skol2 ), skol1 ) ) ==> multiplication( domain(
% 24.83/25.25 skol2 ), skol1 ) }.
% 24.83/25.25 parent0: (54637) {G0,W11,D5,L1,V0,M1} { ! addition( skol1, multiplication
% 24.83/25.25 ( domain( skol2 ), skol1 ) ) = multiplication( domain( skol2 ), skol1 )
% 24.83/25.25 }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54814) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X ), one )
% 24.83/25.25 }.
% 24.83/25.25 parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 24.83/25.25 one }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54815) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X )
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 24.83/25.25 }.
% 24.83/25.25 parent1[0; 2]: (54814) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X )
% 24.83/25.25 , one ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := domain( X )
% 24.83/25.25 Y := one
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54818) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 24.83/25.25 }.
% 24.83/25.25 parent0[0]: (54815) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X
% 24.83/25.25 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (21) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X )
% 24.83/25.25 ) ==> one }.
% 24.83/25.25 parent0: (54818) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==>
% 24.83/25.25 one }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54820) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 24.83/25.25 addition( X, addition( Y, Z ) ) }.
% 24.83/25.25 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 24.83/25.25 ==> addition( addition( Z, Y ), X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Z
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54826) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 24.83/25.25 addition( X, Y ) }.
% 24.83/25.25 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 24.83/25.25 parent1[0; 8]: (54820) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 24.83/25.25 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (24) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ),
% 24.83/25.25 X ) ==> addition( Y, X ) }.
% 24.83/25.25 parent0: (54826) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 24.83/25.25 addition( X, Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54831) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 24.83/25.25 addition( X, addition( Y, Z ) ) }.
% 24.83/25.25 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 24.83/25.25 ==> addition( addition( Z, Y ), X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Z
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54834) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 24.83/25.25 ==> addition( addition( Y, Z ), X ) }.
% 24.83/25.25 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 24.83/25.25 }.
% 24.83/25.25 parent1[0; 6]: (54831) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 24.83/25.25 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := addition( Y, Z )
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (25) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 24.83/25.25 , Z ) = addition( addition( Y, Z ), X ) }.
% 24.83/25.25 parent0: (54834) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 24.83/25.25 ==> addition( addition( Y, Z ), X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54848) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 24.83/25.25 Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54849) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 24.83/25.25 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 resolution: (54850) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 24.83/25.25 parent0[0]: (54848) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 24.83/25.25 , Y ) }.
% 24.83/25.25 parent1[0]: (54849) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (31) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 24.83/25.25 parent0: (54850) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54851) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 24.83/25.25 Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54852) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 24.83/25.25 }.
% 24.83/25.25 parent1[0; 3]: (54851) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 24.83/25.25 ( X, Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54855) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (54852) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 24.83/25.25 , X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (35) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 24.83/25.25 leq( X, Y ) }.
% 24.83/25.25 parent0: (54855) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 24.83/25.25 ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 1 ==> 1
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54857) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 24.83/25.25 Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54858) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 24.83/25.25 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 24.83/25.25 multiplication( X, Y ) ) }.
% 24.83/25.25 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 24.83/25.25 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 24.83/25.25 parent1[0; 5]: (54857) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 24.83/25.25 ( X, Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Z
% 24.83/25.25 Z := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := multiplication( X, Z )
% 24.83/25.25 Y := multiplication( X, Y )
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54859) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 24.83/25.25 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 24.83/25.25 multiplication( X, Y ) ) }.
% 24.83/25.25 parent0[0]: (54858) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 24.83/25.25 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 24.83/25.25 multiplication( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (38) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 24.83/25.25 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 24.83/25.25 ), multiplication( X, Z ) ) }.
% 24.83/25.25 parent0: (54859) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 24.83/25.25 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 24.83/25.25 multiplication( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Z
% 24.83/25.25 Z := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 1 ==> 1
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54861) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 24.83/25.25 addition( X, addition( Y, Z ) ) }.
% 24.83/25.25 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 24.83/25.25 ==> addition( addition( Z, Y ), X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Z
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54867) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z )
% 24.83/25.25 ==> addition( X, Z ), ! leq( Y, Z ) }.
% 24.83/25.25 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 24.83/25.25 ==> Y }.
% 24.83/25.25 parent1[0; 8]: (54861) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 24.83/25.25 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := Z
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (51) {G1,W12,D4,L2,V3,M2} P(11,1) { addition( addition( Z, X )
% 24.83/25.25 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 24.83/25.25 parent0: (54867) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z )
% 24.83/25.25 ==> addition( X, Z ), ! leq( Y, Z ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Z
% 24.83/25.25 Y := X
% 24.83/25.25 Z := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 1 ==> 1
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54914) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 24.83/25.25 ==> Y }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54915) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 24.83/25.25 }.
% 24.83/25.25 parent1[0; 2]: (54914) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 24.83/25.25 ( X, Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54918) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (54915) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 24.83/25.25 , X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (53) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 24.83/25.25 leq( X, Y ) }.
% 24.83/25.25 parent0: (54918) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 24.83/25.25 ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 1 ==> 1
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54920) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 24.83/25.25 Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54921) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 24.83/25.25 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 24.83/25.25 multiplication( X, Y ) ) }.
% 24.83/25.25 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 24.83/25.25 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 24.83/25.25 parent1[0; 5]: (54920) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 24.83/25.25 ( X, Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Z
% 24.83/25.25 Y := X
% 24.83/25.25 Z := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := multiplication( Z, Y )
% 24.83/25.25 Y := multiplication( X, Y )
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54922) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 24.83/25.25 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 24.83/25.25 multiplication( X, Y ) ) }.
% 24.83/25.25 parent0[0]: (54921) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 24.83/25.25 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 24.83/25.25 multiplication( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (78) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 24.83/25.25 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 24.83/25.25 multiplication( Z, Y ) ) }.
% 24.83/25.25 parent0: (54922) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 24.83/25.25 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 24.83/25.25 multiplication( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Z
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 1 ==> 1
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54924) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 24.83/25.25 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 24.83/25.25 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 24.83/25.25 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Z
% 24.83/25.25 Z := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54925) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, X )
% 24.83/25.25 , Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 24.83/25.25 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 24.83/25.25 parent1[0; 7]: (54924) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 24.83/25.25 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 24.83/25.25 }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := one
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54927) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y )
% 24.83/25.25 ) ==> multiplication( addition( one, X ), Y ) }.
% 24.83/25.25 parent0[0]: (54925) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one,
% 24.83/25.25 X ), Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (81) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 24.83/25.25 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 24.83/25.25 parent0: (54927) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y
% 24.83/25.25 ) ) ==> multiplication( addition( one, X ), Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54930) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) )
% 24.83/25.25 ==> domain( multiplication( X, domain( Y ) ) ) }.
% 24.83/25.25 parent0[0]: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 24.83/25.25 ( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54933) {G1,W8,D4,L1,V1,M1} { domain( multiplication( one, X ) )
% 24.83/25.25 ==> domain( domain( X ) ) }.
% 24.83/25.25 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 24.83/25.25 parent1[0; 6]: (54930) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y
% 24.83/25.25 ) ) ==> domain( multiplication( X, domain( Y ) ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := domain( X )
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := one
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54935) {G1,W6,D4,L1,V1,M1} { domain( X ) ==> domain( domain( X )
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 24.83/25.25 parent1[0; 2]: (54933) {G1,W8,D4,L1,V1,M1} { domain( multiplication( one,
% 24.83/25.25 X ) ) ==> domain( domain( X ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54936) {G1,W6,D4,L1,V1,M1} { domain( domain( X ) ) ==> domain( X
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (54935) {G1,W6,D4,L1,V1,M1} { domain( X ) ==> domain( domain(
% 24.83/25.25 X ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (141) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) )
% 24.83/25.25 ==> domain( X ) }.
% 24.83/25.25 parent0: (54936) {G1,W6,D4,L1,V1,M1} { domain( domain( X ) ) ==> domain( X
% 24.83/25.25 ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54937) {G0,W11,D5,L1,V0,M1} { ! multiplication( domain( skol2 ),
% 24.83/25.25 skol1 ) ==> addition( skol1, multiplication( domain( skol2 ), skol1 ) )
% 24.83/25.25 }.
% 24.83/25.25 parent0[0]: (19) {G0,W11,D5,L1,V0,M1} I { ! addition( skol1, multiplication
% 24.83/25.25 ( domain( skol2 ), skol1 ) ) ==> multiplication( domain( skol2 ), skol1 )
% 24.83/25.25 }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54938) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 24.83/25.25 ==> Y }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 resolution: (54939) {G1,W6,D4,L1,V0,M1} { ! leq( skol1, multiplication(
% 24.83/25.25 domain( skol2 ), skol1 ) ) }.
% 24.83/25.25 parent0[0]: (54937) {G0,W11,D5,L1,V0,M1} { ! multiplication( domain( skol2
% 24.83/25.25 ), skol1 ) ==> addition( skol1, multiplication( domain( skol2 ), skol1 )
% 24.83/25.25 ) }.
% 24.83/25.25 parent1[0]: (54938) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 24.83/25.25 , Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := skol1
% 24.83/25.25 Y := multiplication( domain( skol2 ), skol1 )
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (199) {G1,W6,D4,L1,V0,M1} R(19,11) { ! leq( skol1,
% 24.83/25.25 multiplication( domain( skol2 ), skol1 ) ) }.
% 24.83/25.25 parent0: (54939) {G1,W6,D4,L1,V0,M1} { ! leq( skol1, multiplication(
% 24.83/25.25 domain( skol2 ), skol1 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54940) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 24.83/25.25 addition( X, Y ), Y ) }.
% 24.83/25.25 parent0[0]: (24) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 24.83/25.25 ) ==> addition( Y, X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54941) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (35) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 24.83/25.25 leq( X, Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 resolution: (54942) {G2,W5,D3,L1,V2,M1} { leq( Y, addition( X, Y ) ) }.
% 24.83/25.25 parent0[0]: (54941) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 24.83/25.25 , X ) }.
% 24.83/25.25 parent1[0]: (54940) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 24.83/25.25 addition( X, Y ), Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := addition( X, Y )
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (251) {G2,W5,D3,L1,V2,M1} R(24,35) { leq( X, addition( Y, X )
% 24.83/25.25 ) }.
% 24.83/25.25 parent0: (54942) {G2,W5,D3,L1,V2,M1} { leq( Y, addition( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54943) {G1,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 24.83/25.25 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 24.83/25.25 }.
% 24.83/25.25 parent1[0; 2]: (251) {G2,W5,D3,L1,V2,M1} R(24,35) { leq( X, addition( Y, X
% 24.83/25.25 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (263) {G3,W5,D3,L1,V2,M1} P(0,251) { leq( Y, addition( Y, X )
% 24.83/25.25 ) }.
% 24.83/25.25 parent0: (54943) {G1,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54946) {G1,W7,D4,L1,V2,M1} { leq( domain( X ), domain( addition
% 24.83/25.25 ( X, Y ) ) ) }.
% 24.83/25.25 parent0[0]: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 24.83/25.25 ) ) ==> domain( addition( X, Y ) ) }.
% 24.83/25.25 parent1[0; 3]: (263) {G3,W5,D3,L1,V2,M1} P(0,251) { leq( Y, addition( Y, X
% 24.83/25.25 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := domain( Y )
% 24.83/25.25 Y := domain( X )
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (266) {G4,W7,D4,L1,V2,M1} P(17,263) { leq( domain( X ), domain
% 24.83/25.25 ( addition( X, Y ) ) ) }.
% 24.83/25.25 parent0: (54946) {G1,W7,D4,L1,V2,M1} { leq( domain( X ), domain( addition
% 24.83/25.25 ( X, Y ) ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54947) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 24.83/25.25 addition( addition( X, Y ), Z ) }.
% 24.83/25.25 parent0[0]: (25) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 24.83/25.25 Z ) = addition( addition( Y, Z ), X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54948) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 24.83/25.25 , Z ) ) }.
% 24.83/25.25 parent0[0]: (54947) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 24.83/25.25 = addition( addition( X, Y ), Z ) }.
% 24.83/25.25 parent1[0; 2]: (251) {G2,W5,D3,L1,V2,M1} R(24,35) { leq( X, addition( Y, X
% 24.83/25.25 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 Y := addition( Y, Z )
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54949) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 24.83/25.25 , Y ) ) }.
% 24.83/25.25 parent0[0]: (54947) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 24.83/25.25 = addition( addition( X, Y ), Z ) }.
% 24.83/25.25 parent1[0; 2]: (54948) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 24.83/25.25 , Y ), Z ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Z
% 24.83/25.25 Y := X
% 24.83/25.25 Z := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (286) {G3,W7,D4,L1,V3,M1} P(25,251) { leq( Z, addition(
% 24.83/25.25 addition( Y, Z ), X ) ) }.
% 24.83/25.25 parent0: (54949) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 24.83/25.25 , Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Z
% 24.83/25.25 Y := X
% 24.83/25.25 Z := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54952) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 24.83/25.25 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 24.83/25.25 multiplication( X, Z ) ) }.
% 24.83/25.25 parent0[0]: (38) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 24.83/25.25 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 24.83/25.25 ), multiplication( X, Z ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54953) {G1,W17,D3,L3,V3,M3} { ! multiplication( X, Y ) ==>
% 24.83/25.25 multiplication( X, Y ), ! leq( Z, Y ), leq( multiplication( X, Z ),
% 24.83/25.25 multiplication( X, Y ) ) }.
% 24.83/25.25 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 24.83/25.25 ==> Y }.
% 24.83/25.25 parent1[0; 7]: (54952) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 24.83/25.25 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 24.83/25.25 multiplication( X, Z ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Z
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Z
% 24.83/25.25 Z := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqrefl: (54954) {G0,W10,D3,L2,V3,M2} { ! leq( Z, Y ), leq( multiplication
% 24.83/25.25 ( X, Z ), multiplication( X, Y ) ) }.
% 24.83/25.25 parent0[0]: (54953) {G1,W17,D3,L3,V3,M3} { ! multiplication( X, Y ) ==>
% 24.83/25.25 multiplication( X, Y ), ! leq( Z, Y ), leq( multiplication( X, Z ),
% 24.83/25.25 multiplication( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (420) {G2,W10,D3,L2,V3,M2} P(11,38);q { leq( multiplication( Z
% 24.83/25.25 , X ), multiplication( Z, Y ) ), ! leq( X, Y ) }.
% 24.83/25.25 parent0: (54954) {G0,W10,D3,L2,V3,M2} { ! leq( Z, Y ), leq( multiplication
% 24.83/25.25 ( X, Z ), multiplication( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Z
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 1
% 24.83/25.25 1 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54956) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 24.83/25.25 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 24.83/25.25 multiplication( X, Z ) ) }.
% 24.83/25.25 parent0[0]: (38) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 24.83/25.25 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 24.83/25.25 ), multiplication( X, Z ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54958) {G1,W15,D4,L2,V2,M2} { ! multiplication( X, one ) ==>
% 24.83/25.25 multiplication( X, one ), leq( multiplication( X, domain( Y ) ),
% 24.83/25.25 multiplication( X, one ) ) }.
% 24.83/25.25 parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 24.83/25.25 one }.
% 24.83/25.25 parent1[0; 7]: (54956) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 24.83/25.25 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 24.83/25.25 multiplication( X, Z ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 Y := domain( Y )
% 24.83/25.25 Z := one
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqrefl: (54959) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, domain( Y )
% 24.83/25.25 ), multiplication( X, one ) ) }.
% 24.83/25.25 parent0[0]: (54958) {G1,W15,D4,L2,V2,M2} { ! multiplication( X, one ) ==>
% 24.83/25.25 multiplication( X, one ), leq( multiplication( X, domain( Y ) ),
% 24.83/25.25 multiplication( X, one ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54960) {G1,W6,D4,L1,V2,M1} { leq( multiplication( X, domain( Y )
% 24.83/25.25 ), X ) }.
% 24.83/25.25 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 24.83/25.25 parent1[0; 5]: (54959) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X,
% 24.83/25.25 domain( Y ) ), multiplication( X, one ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (422) {G2,W6,D4,L1,V2,M1} P(15,38);q;d(5) { leq(
% 24.83/25.25 multiplication( Y, domain( X ) ), Y ) }.
% 24.83/25.25 parent0: (54960) {G1,W6,D4,L1,V2,M1} { leq( multiplication( X, domain( Y )
% 24.83/25.25 ), X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54961) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (53) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 24.83/25.25 leq( X, Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54963) {G1,W9,D2,L3,V2,M3} { X ==> Y, ! leq( X, Y ), ! leq( Y, X
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 24.83/25.25 ==> Y }.
% 24.83/25.25 parent1[0; 2]: (54961) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq
% 24.83/25.25 ( Y, X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (806) {G2,W9,D2,L3,V2,M3} P(53,11) { ! leq( X, Y ), X = Y, !
% 24.83/25.25 leq( Y, X ) }.
% 24.83/25.25 parent0: (54963) {G1,W9,D2,L3,V2,M3} { X ==> Y, ! leq( X, Y ), ! leq( Y, X
% 24.83/25.25 ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 1
% 24.83/25.25 1 ==> 0
% 24.83/25.25 2 ==> 2
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54966) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq(
% 24.83/25.25 X, Z ) }.
% 24.83/25.25 parent0[0]: (51) {G1,W12,D4,L2,V3,M2} P(11,1) { addition( addition( Z, X )
% 24.83/25.25 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 24.83/25.25 parent1[0; 2]: (286) {G3,W7,D4,L1,V3,M1} P(25,251) { leq( Z, addition(
% 24.83/25.25 addition( Y, Z ), X ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Z
% 24.83/25.25 Z := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := Z
% 24.83/25.25 Y := Y
% 24.83/25.25 Z := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (906) {G4,W8,D3,L2,V3,M2} P(51,286) { leq( Y, addition( X, Z )
% 24.83/25.25 ), ! leq( Y, Z ) }.
% 24.83/25.25 parent0: (54966) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq(
% 24.83/25.25 X, Z ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 Z := Z
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 1 ==> 1
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54971) {G2,W5,D3,L1,V0,M1} { leq( domain( skol1 ), domain( skol2
% 24.83/25.25 ) ) }.
% 24.83/25.25 parent0[0]: (18) {G1,W7,D4,L1,V0,M1} I;d(17) { domain( addition( skol1,
% 24.83/25.25 skol2 ) ) ==> domain( skol2 ) }.
% 24.83/25.25 parent1[0; 3]: (266) {G4,W7,D4,L1,V2,M1} P(17,263) { leq( domain( X ),
% 24.83/25.25 domain( addition( X, Y ) ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := skol1
% 24.83/25.25 Y := skol2
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (1089) {G5,W5,D3,L1,V0,M1} P(18,266) { leq( domain( skol1 ),
% 24.83/25.25 domain( skol2 ) ) }.
% 24.83/25.25 parent0: (54971) {G2,W5,D3,L1,V0,M1} { leq( domain( skol1 ), domain( skol2
% 24.83/25.25 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54973) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 24.83/25.25 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 24.83/25.25 multiplication( Y, Z ) ) }.
% 24.83/25.25 parent0[0]: (78) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 24.83/25.25 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 24.83/25.25 multiplication( Z, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Z
% 24.83/25.25 Z := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54975) {G1,W15,D4,L2,V2,M2} { ! multiplication( one, X ) ==>
% 24.83/25.25 multiplication( one, X ), leq( multiplication( domain( Y ), X ),
% 24.83/25.25 multiplication( one, X ) ) }.
% 24.83/25.25 parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 24.83/25.25 one }.
% 24.83/25.25 parent1[0; 6]: (54973) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 24.83/25.25 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 24.83/25.25 multiplication( Y, Z ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := domain( Y )
% 24.83/25.25 Y := one
% 24.83/25.25 Z := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqrefl: (54976) {G0,W8,D4,L1,V2,M1} { leq( multiplication( domain( Y ), X
% 24.83/25.25 ), multiplication( one, X ) ) }.
% 24.83/25.25 parent0[0]: (54975) {G1,W15,D4,L2,V2,M2} { ! multiplication( one, X ) ==>
% 24.83/25.25 multiplication( one, X ), leq( multiplication( domain( Y ), X ),
% 24.83/25.25 multiplication( one, X ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54977) {G1,W6,D4,L1,V2,M1} { leq( multiplication( domain( X ), Y
% 24.83/25.25 ), Y ) }.
% 24.83/25.25 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 24.83/25.25 parent1[0; 5]: (54976) {G0,W8,D4,L1,V2,M1} { leq( multiplication( domain(
% 24.83/25.25 Y ), X ), multiplication( one, X ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (1532) {G2,W6,D4,L1,V2,M1} P(15,78);q;d(6) { leq(
% 24.83/25.25 multiplication( domain( X ), Y ), Y ) }.
% 24.83/25.25 parent0: (54977) {G1,W6,D4,L1,V2,M1} { leq( multiplication( domain( X ), Y
% 24.83/25.25 ), Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54978) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (53) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 24.83/25.25 leq( X, Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 resolution: (54979) {G2,W8,D5,L1,V2,M1} { X ==> addition( X,
% 24.83/25.25 multiplication( domain( Y ), X ) ) }.
% 24.83/25.25 parent0[1]: (54978) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 24.83/25.25 , X ) }.
% 24.83/25.25 parent1[0]: (1532) {G2,W6,D4,L1,V2,M1} P(15,78);q;d(6) { leq(
% 24.83/25.25 multiplication( domain( X ), Y ), Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := multiplication( domain( Y ), X )
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54980) {G2,W8,D5,L1,V2,M1} { addition( X, multiplication( domain
% 24.83/25.25 ( Y ), X ) ) ==> X }.
% 24.83/25.25 parent0[0]: (54979) {G2,W8,D5,L1,V2,M1} { X ==> addition( X,
% 24.83/25.25 multiplication( domain( Y ), X ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (1539) {G3,W8,D5,L1,V2,M1} R(1532,53) { addition( X,
% 24.83/25.25 multiplication( domain( Y ), X ) ) ==> X }.
% 24.83/25.25 parent0: (54980) {G2,W8,D5,L1,V2,M1} { addition( X, multiplication( domain
% 24.83/25.25 ( Y ), X ) ) ==> X }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54981) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, Y )
% 24.83/25.25 , X ) = addition( X, multiplication( Y, X ) ) }.
% 24.83/25.25 parent0[0]: (81) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 24.83/25.25 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54986) {G1,W11,D5,L1,V1,M1} { multiplication( addition( one,
% 24.83/25.25 domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 24.83/25.25 parent0[0]: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 24.83/25.25 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 24.83/25.25 parent1[0; 7]: (54981) {G1,W11,D4,L1,V2,M1} { multiplication( addition(
% 24.83/25.25 one, Y ), X ) = addition( X, multiplication( Y, X ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 Y := domain( X )
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54987) {G2,W8,D4,L1,V1,M1} { multiplication( one, X ) =
% 24.83/25.25 multiplication( domain( X ), X ) }.
% 24.83/25.25 parent0[0]: (21) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) )
% 24.83/25.25 ==> one }.
% 24.83/25.25 parent1[0; 2]: (54986) {G1,W11,D5,L1,V1,M1} { multiplication( addition(
% 24.83/25.25 one, domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54988) {G1,W6,D4,L1,V1,M1} { X = multiplication( domain( X ), X
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 24.83/25.25 parent1[0; 1]: (54987) {G2,W8,D4,L1,V1,M1} { multiplication( one, X ) =
% 24.83/25.25 multiplication( domain( X ), X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54989) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X ) = X
% 24.83/25.25 }.
% 24.83/25.25 parent0[0]: (54988) {G1,W6,D4,L1,V1,M1} { X = multiplication( domain( X )
% 24.83/25.25 , X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (1695) {G2,W6,D4,L1,V1,M1} P(81,13);d(21);d(6) {
% 24.83/25.25 multiplication( domain( X ), X ) ==> X }.
% 24.83/25.25 parent0: (54989) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X ) =
% 24.83/25.25 X }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54991) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( domain( X ), X
% 24.83/25.25 ) }.
% 24.83/25.25 parent0[0]: (1695) {G2,W6,D4,L1,V1,M1} P(81,13);d(21);d(6) { multiplication
% 24.83/25.25 ( domain( X ), X ) ==> X }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54992) {G2,W8,D4,L1,V1,M1} { domain( X ) ==> multiplication(
% 24.83/25.25 domain( X ), domain( X ) ) }.
% 24.83/25.25 parent0[0]: (141) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) )
% 24.83/25.25 ==> domain( X ) }.
% 24.83/25.25 parent1[0; 4]: (54991) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( domain
% 24.83/25.25 ( X ), X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := domain( X )
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (54993) {G2,W8,D4,L1,V1,M1} { multiplication( domain( X ), domain
% 24.83/25.25 ( X ) ) ==> domain( X ) }.
% 24.83/25.25 parent0[0]: (54992) {G2,W8,D4,L1,V1,M1} { domain( X ) ==> multiplication(
% 24.83/25.25 domain( X ), domain( X ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (1722) {G3,W8,D4,L1,V1,M1} P(141,1695) { multiplication(
% 24.83/25.25 domain( X ), domain( X ) ) ==> domain( X ) }.
% 24.83/25.25 parent0: (54993) {G2,W8,D4,L1,V1,M1} { multiplication( domain( X ), domain
% 24.83/25.25 ( X ) ) ==> domain( X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54995) {G4,W9,D4,L2,V3,M2} { leq( X, Y ), ! leq( X,
% 24.83/25.25 multiplication( domain( Z ), Y ) ) }.
% 24.83/25.25 parent0[0]: (1539) {G3,W8,D5,L1,V2,M1} R(1532,53) { addition( X,
% 24.83/25.25 multiplication( domain( Y ), X ) ) ==> X }.
% 24.83/25.25 parent1[0; 2]: (906) {G4,W8,D3,L2,V3,M2} P(51,286) { leq( Y, addition( X, Z
% 24.83/25.25 ) ), ! leq( Y, Z ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := Z
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := Y
% 24.83/25.25 Y := X
% 24.83/25.25 Z := multiplication( domain( Z ), Y )
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (6325) {G5,W9,D4,L2,V3,M2} P(1539,906) { leq( Z, X ), ! leq( Z
% 24.83/25.25 , multiplication( domain( Y ), X ) ) }.
% 24.83/25.25 parent0: (54995) {G4,W9,D4,L2,V3,M2} { leq( X, Y ), ! leq( X,
% 24.83/25.25 multiplication( domain( Z ), Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := Z
% 24.83/25.25 Y := X
% 24.83/25.25 Z := Y
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 1 ==> 1
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 resolution: (54996) {G3,W9,D4,L1,V1,M1} { leq( multiplication( X, domain(
% 24.83/25.25 skol1 ) ), multiplication( X, domain( skol2 ) ) ) }.
% 24.83/25.25 parent0[1]: (420) {G2,W10,D3,L2,V3,M2} P(11,38);q { leq( multiplication( Z
% 24.83/25.25 , X ), multiplication( Z, Y ) ), ! leq( X, Y ) }.
% 24.83/25.25 parent1[0]: (1089) {G5,W5,D3,L1,V0,M1} P(18,266) { leq( domain( skol1 ),
% 24.83/25.25 domain( skol2 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := domain( skol1 )
% 24.83/25.25 Y := domain( skol2 )
% 24.83/25.25 Z := X
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (20864) {G6,W9,D4,L1,V1,M1} R(420,1089) { leq( multiplication
% 24.83/25.25 ( X, domain( skol1 ) ), multiplication( X, domain( skol2 ) ) ) }.
% 24.83/25.25 parent0: (54996) {G3,W9,D4,L1,V1,M1} { leq( multiplication( X, domain(
% 24.83/25.25 skol1 ) ), multiplication( X, domain( skol2 ) ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (54998) {G4,W8,D4,L1,V0,M1} { leq( domain( skol1 ),
% 24.83/25.25 multiplication( domain( skol1 ), domain( skol2 ) ) ) }.
% 24.83/25.25 parent0[0]: (1722) {G3,W8,D4,L1,V1,M1} P(141,1695) { multiplication( domain
% 24.83/25.25 ( X ), domain( X ) ) ==> domain( X ) }.
% 24.83/25.25 parent1[0; 1]: (20864) {G6,W9,D4,L1,V1,M1} R(420,1089) { leq(
% 24.83/25.25 multiplication( X, domain( skol1 ) ), multiplication( X, domain( skol2 )
% 24.83/25.25 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := skol1
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := domain( skol1 )
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (25587) {G7,W8,D4,L1,V0,M1} P(1722,20864) { leq( domain( skol1
% 24.83/25.25 ), multiplication( domain( skol1 ), domain( skol2 ) ) ) }.
% 24.83/25.25 parent0: (54998) {G4,W8,D4,L1,V0,M1} { leq( domain( skol1 ),
% 24.83/25.25 multiplication( domain( skol1 ), domain( skol2 ) ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 resolution: (55000) {G3,W16,D4,L2,V0,M2} { domain( skol1 ) =
% 24.83/25.25 multiplication( domain( skol1 ), domain( skol2 ) ), ! leq( multiplication
% 24.83/25.25 ( domain( skol1 ), domain( skol2 ) ), domain( skol1 ) ) }.
% 24.83/25.25 parent0[0]: (806) {G2,W9,D2,L3,V2,M3} P(53,11) { ! leq( X, Y ), X = Y, !
% 24.83/25.25 leq( Y, X ) }.
% 24.83/25.25 parent1[0]: (25587) {G7,W8,D4,L1,V0,M1} P(1722,20864) { leq( domain( skol1
% 24.83/25.25 ), multiplication( domain( skol1 ), domain( skol2 ) ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := domain( skol1 )
% 24.83/25.25 Y := multiplication( domain( skol1 ), domain( skol2 ) )
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 resolution: (55002) {G3,W8,D4,L1,V0,M1} { domain( skol1 ) = multiplication
% 24.83/25.25 ( domain( skol1 ), domain( skol2 ) ) }.
% 24.83/25.25 parent0[1]: (55000) {G3,W16,D4,L2,V0,M2} { domain( skol1 ) =
% 24.83/25.25 multiplication( domain( skol1 ), domain( skol2 ) ), ! leq( multiplication
% 24.83/25.25 ( domain( skol1 ), domain( skol2 ) ), domain( skol1 ) ) }.
% 24.83/25.25 parent1[0]: (422) {G2,W6,D4,L1,V2,M1} P(15,38);q;d(5) { leq( multiplication
% 24.83/25.25 ( Y, domain( X ) ), Y ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := skol2
% 24.83/25.25 Y := domain( skol1 )
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (55003) {G3,W8,D4,L1,V0,M1} { multiplication( domain( skol1 ),
% 24.83/25.25 domain( skol2 ) ) = domain( skol1 ) }.
% 24.83/25.25 parent0[0]: (55002) {G3,W8,D4,L1,V0,M1} { domain( skol1 ) = multiplication
% 24.83/25.25 ( domain( skol1 ), domain( skol2 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (25618) {G8,W8,D4,L1,V0,M1} R(25587,806);r(422) {
% 24.83/25.25 multiplication( domain( skol1 ), domain( skol2 ) ) ==> domain( skol1 )
% 24.83/25.25 }.
% 24.83/25.25 parent0: (55003) {G3,W8,D4,L1,V0,M1} { multiplication( domain( skol1 ),
% 24.83/25.25 domain( skol2 ) ) = domain( skol1 ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 eqswap: (55005) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) )
% 24.83/25.25 ==> domain( multiplication( X, domain( Y ) ) ) }.
% 24.83/25.25 parent0[0]: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 24.83/25.25 ( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 Y := Y
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (55008) {G1,W9,D5,L1,V0,M1} { domain( multiplication( domain(
% 24.83/25.25 skol1 ), skol2 ) ) ==> domain( domain( skol1 ) ) }.
% 24.83/25.25 parent0[0]: (25618) {G8,W8,D4,L1,V0,M1} R(25587,806);r(422) {
% 24.83/25.25 multiplication( domain( skol1 ), domain( skol2 ) ) ==> domain( skol1 )
% 24.83/25.25 }.
% 24.83/25.25 parent1[0; 7]: (55005) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y
% 24.83/25.25 ) ) ==> domain( multiplication( X, domain( Y ) ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := domain( skol1 )
% 24.83/25.25 Y := skol2
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (55009) {G2,W8,D5,L1,V0,M1} { domain( multiplication( domain(
% 24.83/25.25 skol1 ), skol2 ) ) ==> domain( skol1 ) }.
% 24.83/25.25 parent0[0]: (141) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) )
% 24.83/25.25 ==> domain( X ) }.
% 24.83/25.25 parent1[0; 6]: (55008) {G1,W9,D5,L1,V0,M1} { domain( multiplication(
% 24.83/25.25 domain( skol1 ), skol2 ) ) ==> domain( domain( skol1 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := skol1
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (25882) {G9,W8,D5,L1,V0,M1} P(25618,14);d(141) { domain(
% 24.83/25.25 multiplication( domain( skol1 ), skol2 ) ) ==> domain( skol1 ) }.
% 24.83/25.25 parent0: (55009) {G2,W8,D5,L1,V0,M1} { domain( multiplication( domain(
% 24.83/25.25 skol1 ), skol2 ) ) ==> domain( skol1 ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 resolution: (55012) {G2,W9,D5,L1,V1,M1} { ! leq( skol1, multiplication(
% 24.83/25.25 domain( X ), multiplication( domain( skol2 ), skol1 ) ) ) }.
% 24.83/25.25 parent0[0]: (199) {G1,W6,D4,L1,V0,M1} R(19,11) { ! leq( skol1,
% 24.83/25.25 multiplication( domain( skol2 ), skol1 ) ) }.
% 24.83/25.25 parent1[0]: (6325) {G5,W9,D4,L2,V3,M2} P(1539,906) { leq( Z, X ), ! leq( Z
% 24.83/25.25 , multiplication( domain( Y ), X ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := multiplication( domain( skol2 ), skol1 )
% 24.83/25.25 Y := X
% 24.83/25.25 Z := skol1
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (55013) {G1,W9,D5,L1,V1,M1} { ! leq( skol1, multiplication(
% 24.83/25.25 multiplication( domain( X ), domain( skol2 ) ), skol1 ) ) }.
% 24.83/25.25 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 24.83/25.25 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 24.83/25.25 parent1[0; 3]: (55012) {G2,W9,D5,L1,V1,M1} { ! leq( skol1, multiplication
% 24.83/25.25 ( domain( X ), multiplication( domain( skol2 ), skol1 ) ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := domain( X )
% 24.83/25.25 Y := domain( skol2 )
% 24.83/25.25 Z := skol1
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (29163) {G6,W9,D5,L1,V1,M1} R(6325,199);d(4) { ! leq( skol1,
% 24.83/25.25 multiplication( multiplication( domain( X ), domain( skol2 ) ), skol1 ) )
% 24.83/25.25 }.
% 24.83/25.25 parent0: (55013) {G1,W9,D5,L1,V1,M1} { ! leq( skol1, multiplication(
% 24.83/25.25 multiplication( domain( X ), domain( skol2 ) ), skol1 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := X
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 0 ==> 0
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (55017) {G7,W9,D5,L1,V0,M1} { ! leq( skol1, multiplication(
% 24.83/25.25 multiplication( domain( skol1 ), domain( skol2 ) ), skol1 ) ) }.
% 24.83/25.25 parent0[0]: (25882) {G9,W8,D5,L1,V0,M1} P(25618,14);d(141) { domain(
% 24.83/25.25 multiplication( domain( skol1 ), skol2 ) ) ==> domain( skol1 ) }.
% 24.83/25.25 parent1[0; 5]: (29163) {G6,W9,D5,L1,V1,M1} R(6325,199);d(4) { ! leq( skol1
% 24.83/25.25 , multiplication( multiplication( domain( X ), domain( skol2 ) ), skol1 )
% 24.83/25.25 ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := multiplication( domain( skol1 ), skol2 )
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (55018) {G8,W6,D4,L1,V0,M1} { ! leq( skol1, multiplication(
% 24.83/25.25 domain( skol1 ), skol1 ) ) }.
% 24.83/25.25 parent0[0]: (25618) {G8,W8,D4,L1,V0,M1} R(25587,806);r(422) {
% 24.83/25.25 multiplication( domain( skol1 ), domain( skol2 ) ) ==> domain( skol1 )
% 24.83/25.25 }.
% 24.83/25.25 parent1[0; 4]: (55017) {G7,W9,D5,L1,V0,M1} { ! leq( skol1, multiplication
% 24.83/25.25 ( multiplication( domain( skol1 ), domain( skol2 ) ), skol1 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 paramod: (55019) {G3,W3,D2,L1,V0,M1} { ! leq( skol1, skol1 ) }.
% 24.83/25.25 parent0[0]: (1695) {G2,W6,D4,L1,V1,M1} P(81,13);d(21);d(6) { multiplication
% 24.83/25.25 ( domain( X ), X ) ==> X }.
% 24.83/25.25 parent1[0; 3]: (55018) {G8,W6,D4,L1,V0,M1} { ! leq( skol1, multiplication
% 24.83/25.25 ( domain( skol1 ), skol1 ) ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 X := skol1
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 resolution: (55020) {G2,W0,D0,L0,V0,M0} { }.
% 24.83/25.25 parent0[0]: (55019) {G3,W3,D2,L1,V0,M1} { ! leq( skol1, skol1 ) }.
% 24.83/25.25 parent1[0]: (31) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 substitution1:
% 24.83/25.25 X := skol1
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 subsumption: (54616) {G10,W0,D0,L0,V0,M0} P(25882,29163);d(25618);d(1695);r
% 24.83/25.25 (31) { }.
% 24.83/25.25 parent0: (55020) {G2,W0,D0,L0,V0,M0} { }.
% 24.83/25.25 substitution0:
% 24.83/25.25 end
% 24.83/25.25 permutation0:
% 24.83/25.25 end
% 24.83/25.25
% 24.83/25.25 Proof check complete!
% 24.83/25.25
% 24.83/25.25 Memory use:
% 24.83/25.25
% 24.83/25.25 space for terms: 817691
% 24.83/25.25 space for clauses: 2446527
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 clauses generated: 866901
% 24.83/25.25 clauses kept: 54617
% 24.83/25.25 clauses selected: 1841
% 24.83/25.25 clauses deleted: 4443
% 24.83/25.25 clauses inuse deleted: 57
% 24.83/25.25
% 24.83/25.25 subsentry: 8732437
% 24.83/25.25 literals s-matched: 3449567
% 24.83/25.25 literals matched: 3279735
% 24.83/25.25 full subsumption: 1185742
% 24.83/25.25
% 24.83/25.25 checksum: 967778694
% 24.83/25.25
% 24.83/25.25
% 24.83/25.25 Bliksem ended
%------------------------------------------------------------------------------